490 



BELL SYSTEM TECHNICAL JOURNAL 



Single-Phase Extensions 

 One of the special conditions under which residual currents or 

 voltages (particularly of the non-triple series of harmonics) are set up 

 on a power system is where single-phase circuits are connected metal- 

 lically to 3-phase circuits. With such a connection, the inductive 

 influence of both the single-phase and 3-phase parts of the power circuit 

 may be affected. Briefly the conditions are as follows: 



-r 



Er = OA+OB +0C = 



A BALANCED 

 3 PHASE 



Er = OA + OB= -OC 



B SINGLE PHASE TAKEN 

 FROM 3 PHASE LINE 



Er = OI + 02=0 



C BALANCED 

 SINGLE PHASE 



Fig. 15 — Comparison of residual voltages in perfectly balanced 3-phase line; a single- 

 phase tap from 3-phase line, and a perfectly balanced single-phase line. 



Single-phase portion 



1. On the single-phase portion of the circuit, a residual voltage exists 



which ordinarily is approximately equal to the normal voltage to 

 ground of a phase wire. This is readily evident from an inspec- 

 tion of the vector relations shown on Fig. \S-B. Fig. 15-C 

 shows that there is nothing inherently unbalanced in single- 

 phase circuits; it is only when they are connected directly to a 

 three-phase circuit or have some unbalanced connections that 

 they have residuals on them. 



2. Figure 16 shows schematically the arrangements used to illustrate 



the effects of metallically connecting a single-phase circuit to a 

 three-phase circuit. By throwing the four-pole, double-throw 

 switch, the noise to ground in the miniature telephone circuit 

 (exposed only to the single-phase circuit) with the single-phase 



